On Steenrod $\mathbb{L}$-homology, generalized manifolds, and surgery

Abstract

The aim of this paper is to show the importance of the Steenrod construction of homology theories for the disassembly process in surgery on a generalized $n$-manifold $X^n$, in order to produce an element of generalized homology theory, which is basic for calculations. In particular, we show how to construct an element of the $n$-th Steenrod homology group $H_n^{st}(X^n,{\mathbb{L}}^{+}),$ where ${\mathbb{L}}^{+}$ is the connected covering spectrum of the periodic surgery spectrum $\mathbb{L}$, avoiding the use of the geometric splitting procedure, which is standardly used in surgery on topological manifolds.

Cited by in corpus (1)

• Limits of manifolds in the Gromov-Hausdorff metric space